Lyapunov spectrum of nonautonomous linear Young differential equations
Speaker: Phan Thanh Hồng (Thang Long University)

Time: 14h00, Thursday, September 6, 2018
Location: Room 302, Building A5, Institute of Mathematics
Abstract: We show that a linear Young differential equation generates a topological two-parameter flow, thus the notions of Lyapunov exponents and Lyapunov spectrum are well-defined. The spectrum can be computed using the discretized flow and is independent of the driving path for triangular systems which are regular in the sense of Lyapunov. In the stochastic setting, the system generates a stochastic two-parameter flow which satisfies the integrability condition, hence the Lyapunov exponents are random variables of finite moments. Finally, we derive a Millionshchikov Theorem stating that almost all, in a sense of an invariant measure, linear nonautonomous Young differential equations are Lyapunov regular.

(Joint work with Nguyen Dinh Cong and Luu Hoang Duc).